A305809 Dirichlet convolution of A003415 (Arithmetic derivative) with itself.

0, 0, 0, 1, 0, 2, 0, 8, 1, 2, 0, 18, 0, 2, 2, 40, 0, 22, 0, 22, 2, 2, 0, 96, 1, 2, 12, 26, 0, 40, 0, 160, 2, 2, 2, 147, 0, 2, 2, 128, 0, 48, 0, 34, 28, 2, 0, 400, 1, 34, 2, 38, 0, 156, 2, 160, 2, 2, 0, 276, 0, 2, 32, 560, 2, 64, 0, 46, 2, 56, 0, 680, 0, 2, 36, 50, 2, 72, 0, 560, 90, 2, 0, 348, 2, 2, 2, 224, 0, 346, 2, 58, 2, 2, 2, 1440, 0, 46, 40, 267, 0, 88

Offset

1,6

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = Sum_{d|n} A003415(n/d)*A003415(d).

Prog

(PARI)
A003415(n) = {my(fac); if(n<1, 0, fac=factor(n); sum(i=1, matsize(fac)[1], n*fac[i, 2]/fac[i, 1]))}; \\ From A003415
A305809(n) = sumdiv(n, d, A003415(n/d)*A003415(d));

Crossrefs

Cf. A003415, A300251, A300252.

Cf. A008578 (positions of 0's), A001248 (of 1's), A006881 (of 2's).

Sequence in context: A239275 A186745 A109573 * A349139 A159810 A199268

Adjacent sequences: A305806 A305807 A305808 * A305810 A305811 A305812

Keyword

nonn

Author

Antti Karttunen, Jun 13 2018

Status

approved